Placed a metal bar, at a temperature of 100°F in a room with constant temperature of 0°F. After 20 minutes the temperature of the bar is 50°F. Determine the time required to reach the bar at a temperature of 25°F and the temperature of the bar after 10 minutes.
Answer: t = 39.6; T = 70.5 º F.
We can use Newton's Law of Cooling: The temperature T of an object with intial temperature `T_0` after t minutes in a room with ambient temperature `T_r` is given by `T=Ce^(-kt)+T_r` .
Here `T_r=0` . We are given points `(t,T)` as `(0,100);(20,50)`
So `T=100e^(-.035t)` gives the temperature at time t:
(a) If the temperature of the bar is `25^@` find the time t:
So the time required is approximately 39.6 minutes
(b) Find the temperature after 10 minutes:
So the temperature at 10 minutes is approximately `70.5^@`